Stability of the space identification problem for the elliptic‐telegraph differential equation

Abstract

The present paper is devoted to study the space identification problem for the elliptic-telegraph differential equation in Hilbert spaces with the self-adjoint positive definite operator. The main theorem on the stability of the space identification problem for the elliptic-telegraph differential equation is proved. In applications, theorems on the stability of three source identification problems for one dimensional with nonlocal conditions and multidimensional elliptic-telegraph differential equations are established.

An Operator Method for Investigation of the Stability of Time-Dependent Source Identification Telegraph Type Differential Problems

“…in a Hilbert space H with the SAPDO A was investigated in [28]. The well-posedness of the space-dependent SIPs for telegraph and elliptic-telegraph DEs was studied by Ashyralyev and Cekic [42] and by Ashyralyev and Al-Hammouri [43], respectively. In particular, the well-posedness of the source identification problem for a TDE with unknown parameter P…”

“…In applications, three source identification problems for telegraph equations were investigated. In addition, in [43], the authors investigated the source identification problems for the elliptic-telegraph differential equation with unknown parameter P in a Hilbert space with a self-adjoint positive definite operator. In [11], Kozhanov and Safiullaeva studied the solvability of the inverse problems on finding a solution W(τ, η) and an unknown coefficient c for a TDE…”